Numerical Analysis and Floating-Point Representation Quiz

Introduction to Numerical Analysis and Floating-Point Representation

• FMNF10 is a basic course in numerical analysis that covers a range of numerical methods to solve common problems in science and engineering.
• Numerical methods range from generally applicable to highly specialized methods that only work under certain conditions.
• The course's purpose is to introduce students to common concepts in numerical analysis and scientific computing, and the choice of method is less important.
• The course includes four Exercise Sheets and two Projects that require students to test the theory covered during lectures by writing their own codes, preferably in Matlab.
• Matlab skills are important for success in the course, and students are recommended to go through basic Matlab syntax examples available on the course web page.
• Computers use a finite set of approximately 10^19 distinct floating-point numbers, and all other numbers are rounded to one of these numbers, creating rounding errors.
• The absolute error and relative error are used to measure the error introduced by the computer's rounding, with the relative error having a typical upper bound of 2*10^-16.
• The error introduced by rounding can magnify during a computation and destroy all accuracy in the final result.
• Matrix-vector multiplication is a fundamental concept in numerical analysis, with the cost of multiplication being 2n^2 FLOPs to leading order in n when n is large.
• The cost of matrix-vector multiplication is expressed using Big-O notation as O(n^2).
• Sauer covers matrix-vector multiplication in Appendix A.1.
• The understanding of floating-point representation and matrix-vector multiplication is essential for understanding computations in numerical analysis.